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Local Uniqueness of Solutions to Ky Fan Vector Inequalities using Approximations as Derivatives

Author

Listed:
  • P. Q. Khanh

    (International University of Hochiminh City)

  • L. T. Tung

    (Cantho University)

Abstract

We establish sufficient conditions for the local uniqueness of solutions to Ky Fan vector strong and weak inequalities. By using approximations as generalized derivatives, our results are valid even in cases where the maps involved in the problems suffer infinite discontinuity at the considered point. Corollaries and examples show that the results extend and improve existing ones in the literature.

Suggested Citation

  • P. Q. Khanh & L. T. Tung, 2012. "Local Uniqueness of Solutions to Ky Fan Vector Inequalities using Approximations as Derivatives," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 840-854, December.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:3:d:10.1007_s10957-012-0075-9
    DOI: 10.1007/s10957-012-0075-9
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    References listed on IDEAS

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    1. Nguyen Hai & Phan Khanh & Nguyen Quan, 2009. "On the existence of solutions to quasivariational inclusion problems," Computational Optimization and Applications, Springer, vol. 45(4), pages 565-581, December.
    2. L. C. Ceng & A. Petruşel & J. C. Yao, 2009. "Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 37-58, October.
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    5. P. Q. Khanh & N. D. Tuan, 2006. "First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 289-308, August.
    6. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, November.
    7. Le Tuan & Gue Lee & Pham Sach, 2010. "Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones," Journal of Global Optimization, Springer, vol. 47(4), pages 639-660, August.
    8. M.A. Tawhid, 2002. "On the Local Uniqueness of Solutions of Variational Inequalities Under H-Differentiability," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 149-164, April.
    9. D.T. Luc & M.A. Noor, 2003. "Local Uniqueness of Solutions of General Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 103-119, April.
    Full references (including those not matched with items on IDEAS)

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